Solution:
We are left with 3 choices.
Choice 1:
The first choice is to give the contract to M/S Jagan. In this case, we know that Jagan's market reach is 55%. It has been given that the total profit potential is 5 crores in the present year and 15 crores in the next 4 years.
Therefore, the expected value of profit earned for choice 1 is 0.55*(5+15) = Rs.11 crore.
Choice 2:Give the contract to M/s Bola for one year and based on the performance, renew the contract with him for the next 4years or give M/S Jagan the contract for the next 4 years.
Let us assume that M/S Bola retains the contract for all 5 years. Rajat will renew the contract only if M/S Bola's claimthat their market reach is 60% is true. The probability of the claim being true is 0.6.
Therefore, the EV of return if M/S Bola bags the contract for all
5 years = 0.6*0.6*(5+15) = Rs. 7.2 crores.
Let us assume that M/S Bola's claim is false. The probability of the claim being false is 1-0.6 = 0.4.Now, if the claim is false, Rajat will terminate the contract by the end of the year and will partner with M/S Jagan for thenext 4 years. Also, we have historic data that M/S Bola reaches 40% of the customers. Even if the claim is false, the laptops will reach 40% of the customers in the first year and 55% of the customers from the second year (Since M/SJagan will bag the contract).
Therefore, the EV of profit in this case is 0.4*0.4*5+0.4*0.55*15 = 0.8 + 3.3 = Rs.4.1 crores.
Therefore, the total EV if M/S Bola bags the contract the first year is 7.2+4.1 = Rs.11.3 crores.
It has been given in this question that M/S James claims a coverage of 55% and the probability of this being true is 0.7.
Choice 3:Give the contract to M/s James for one year and based on the performance, renew the contract with him for the next 4years or give M/S Jagan the contract for the next 4 years.
Let us assume that M/S James retains the contract for all 5 years. Rajat will renew the contract only if M/S Jame's claimthat their market reach is 55% is true. The probability of the claim being true is 0.7.
Therefore, the EV of return if M/S James bags the contract for all 5 years = 0.7*0.55*(5+15) = Rs. 7.7 crores.
Let us assume that M/S James's claim is false. The probability of the claim being false is 1-0.7 = 0.3.Now, if the claim is false, Rajat will terminate the contract by the end of the year and will partner with M/S Jagan for thenext 4 years. Also, we have historic data that M/S James reaches 25% of the customers. Even if the claim is false, thelaptops will reach 25% of the customers in the first year and 55% of the customers from the second year (Since M/SJagan will bag the contract).
Therefore, the EV of profit in this case is 0.3*0.25*5+0.3*0.55*15 = 0.375 + 2.475 = Rs.2.85 crores.
Therefore, the total EV if M/S Bola bags the contract the first year is 7.7+2.85 = Rs.10.55 crores.
EV of choice 1 = Rs. 11 crores
EV of choice 2 = Rs. 11.3 crores
EV of choice 3 = Rs. 10.55 crores
Arranging the choices by EV, we get, Choice 2 > Choice 1 > Choice 3.
Choice 2 is more profitable than choice 3. Therefore, option B is true and hence, option B is the right answer.
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